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Math Exposition on YouTube

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Re: Math Exposition on YouTube

#21

As a maths graduate from nearly 40 years ago I've forgotten far more than I remember, but really enjoy little 10-15 minute snippets of calculus and analysis on YouTube that tickle the rusty old neurons. Current favourite is Michael "and that's a good place to stop" Penn.

Forgetting so much is my current fear as well. What did you end up doing?

Re: Math Exposition on YouTube

#22

As a maths graduate from nearly 40 years ago I've forgotten far more than I remember, but really enjoy little 10-15 minute snippets of calculus and analysis on YouTube that tickle the rusty old neurons. Current favourite is Michael "and that's a good place to stop" Penn.

I'm the same as you )other than being a Physics graduate). Love Michael Penn. Interesting topics with a good but not pedantic level of rigor.

https://youtube.com/@MichaelPennMath

Re: Math Exposition on YouTube

#23

This is a great explanation of why districts themselves are bad. We need proportional representation with either no districts at all or large multi-member districts.

I'm not sure districts are inherently bad. The concept that people living in the same geographic area will have similar concerns that need to be addressed makes sense to me. I think my preference would be districts defined by geographic features and boundaries paired with a different set of elected officials determined by the type of proportional representation without any limits on geographic boundaries.

You should look into the German system.

How it is supposed to work is that 50% of representatives are 'local' representing a region (of roughly 300.000 people) and the remaining 50% of representatives ensure proportionality.

So, imagine the CDU (centre-right party) wins 40% of the voting share, but 60% of the seats, the SPD (centre-left) 30% of both voting share, and seats, the Greens 20% of the share but only 10% of the seats, and the FDP 10% of the share and no seats. The seats to ensure proportionality would be distributed 20%, 30%, 30%, 20% respectively.

There are a lot of subtleties to the system to ensure true proportionality that I won't go into right now, and tend to lead to the parliament growing (if things work perfectly there should be 598 seats, but currently there are 736), but broadly the system works.

Re: Math Exposition on YouTube

#24

As a maths graduate from nearly 40 years ago I've forgotten far more than I remember, but really enjoy little 10-15 minute snippets of calculus and analysis on YouTube that tickle the rusty old neurons. Current favourite is Michael "and that's a good place to stop" Penn.

Forgetting so much is my current fear as well. What did you end up doing?

It hasn’t been nearly so long for me, but I’ve managed to hold on to much of the math I’ve learned by re-proving theorems I’d learned and solving problems in my head during downtime, while doing household chores, and while falling asleep. Another benefit is that I am almost never bored since there’s always more math to do.

Re: Math Exposition on YouTube

#25

This is a great explanation of why districts themselves are bad. We need proportional representation with either no districts at all or large multi-member districts.

Proportional representation has problems too. There is no perfect system.

> There is no perfect system.

So what? FPTP is objectively the worst voting method, across pretty much all metrics (others may do slightly worse at local representation).

Also, proportional representation is a class of voting methods (my personal preference being STV).

Re: Math Exposition on YouTube

#26
post #12

Earlier quoted context omitted.

I'm not sure districts are inherently bad. The concept that people living in the same geographic area will have similar concerns that need to be addressed makes sense to me. I think my preference would be districts defined by geographic features and boundaries paired with a different set of elected officials determined by the type of proportional representation without any limits on geographic boundaries.

I mean most European countries have some form of districs as well, it is just not a winner takes all approach. Nobody cares how districts are shaped when there is no advantage in having them shaped a certain way. I think the US system is undemocratic as it fails on some very fundamental levels to assure representation that honors the voter's will.

If the shape of the districts were truly irrelevant, what would the advantage of having them be, relative to a single district with proportional representation?

Re: Math Exposition on YouTube

#27
I always thought some aspects of how mathematics is taught has been wrong for a very long time. Part of it, I think, are people working as teachers/professors who are really bad teachers.

As an example: One that stuck in my head from decades ago was solving the Fibonacci recurrent relation. At some point the professor wrote down “r^n” and somehow “r^2 + r + 1 = 0” shows up.

When asked where r^n came from he said it was just a guess. When asked how or why not guess something completely different, he said “that’s how we solve these problems”.

And that was that. Nobody in his class understood this and myriad other areas in math where the answer seems to be “and then a miracle occurs”.

There are many YouTube math teacher who are massively better than most university (and below) instructors. My guess is this is because they actually love what they do.

Re: Math Exposition on YouTube

#28

Earlier quoted context omitted.

I'm not sure districts are inherently bad. The concept that people living in the same geographic area will have similar concerns that need to be addressed makes sense to me. I think my preference would be districts defined by geographic features and boundaries paired with a different set of elected officials determined by the type of proportional representation without any limits on geographic boundaries.

> he concept that people living in the same geographic area will have similar concerns that need to be addressed makes sense to me. This is true but then there are other buckets as well. Why should location be the only organizing principle, when we know there are a bunch of concerns that aren't tied to it? Why not have virtual districts across dimensions? You get a vote for your birth year cohort, a vote for your geo…

You don't need proportional representation to get away from FPTP. Approval voting and score voting look especially good and they wouldn't require a change to the constitution.

Re: Math Exposition on YouTube

#29

Earlier quoted context omitted.

> he concept that people living in the same geographic area will have similar concerns that need to be addressed makes sense to me. This is true but then there are other buckets as well. Why should location be the only organizing principle, when we know there are a bunch of concerns that aren't tied to it? Why not have virtual districts across dimensions? You get a vote for your birth year cohort, a vote for your geo…

Just think of the gerrymandering opportunities such a system would present...

As long as there's a separate vote for each dimension, this seems like an improvement. Gerrymandering would be significantly harder on age and income, since they're one-dimensional. If age is defined by birth year, then that would have no gerrymandering at all.

Re: Math Exposition on YouTube

#30
post #28

Earlier quoted context omitted.

> he concept that people living in the same geographic area will have similar concerns that need to be addressed makes sense to me. This is true but then there are other buckets as well. Why should location be the only organizing principle, when we know there are a bunch of concerns that aren't tied to it? Why not have virtual districts across dimensions? You get a vote for your birth year cohort, a vote for your geo…

You don't need proportional representation to get away from FPTP. Approval voting and score voting look especially good and they wouldn't require a change to the constitution.

> You don't need proportional representation to get away from FPTP.

But you should, since proprortionality as a property has strong evidence of being practically producing better piblic satisfaction with government, as well as having a strong theoretical argument for being the best measure of the degree to which a “representative” body actually is representative.

> Approval voting and score voting look especially good and they wouldn't require a change to the constitution.

Approval voting and score voting look especially bad for public elections in a multicultural society, since they call for abstract ratings that where there are well-established cultural variations in assignment for the same actual sentiment, and treat them as having consistent meaning.

And rough PR in the House (e.g., by STV) doesn't require a Constitutional amendment, either, only a statutory change.

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